Grease Pencil primitive/shape tools do not function
After some messing about, I deleted my user preferences to find that it solved the issue.
Unsatisfied with this catch-all fix, I endeavored to find out why, and went through each setting, enabling and disabling it to see its effect.
It turns out that my keymap, being the same keymap I've been using for, perhaps years, still being retained through to 2.92, somewhat customized, caused the issue.
I do not know why, or how, but not using it seems to fix the issue entirely.
Perhaps there are some formatting issues, as clearly my old keymap file does not load the same Preferences menu that the new default ones do.
It also seems that it doesn't know what about itself has been changed, as it marks parts of the keymap as being able to be restored, when I did not change those parts. Perhaps the keymap is corrupted.
I have no idea how the keymap having problems would affect the ability of the tools to function, but apparently it does.